By that same logic, shouldn't your rights end at the epidermis on my arm? Don't I have a right to be secure in my person, as that phrase implies? That interpretation makes more sense to me than asserting the right to be exempt from natural biological functions like disease.
I would be totally okay with treating it like a driving accident. You're free not to get the shot, but in the case that you contract Covid you then open yourself up to civil liability to everyone you came in contact with.
Should that be the precedent for all communicable disease going forward? What about the common cold your child gave me that caused me to miss work? Will you be liable for that?
Many people's kids are, in fact, sent to school with communicable diseases that are deadly for some, just as Covid is deadly for some. But why stop at death? If your child's cold costs me a day of work, then by your logic, I should sue you for lost wages.